Evolution of the semiconductor manufacturing industry is placing ever greater demands on yield management and, in particular, on metrology and inspection systems. Critical dimensions continue to shrink. Economics is driving the industry to decrease the time for achieving high-yield, high-value production. Minimizing the total time from detecting a yield problem to fixing it determines the return-on-investment for a semiconductor manufacturer.
Fabricating semiconductor devices, such as logic and memory devices, typically includes processing a semiconductor wafer using a large number of fabrication processes to form various features and multiple levels of the semiconductor devices. For example, lithography is a semiconductor fabrication process that involves transferring a pattern from a reticle to a photoresist arranged on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical-mechanical polishing (CMP), etch, deposition, and ion implantation. Multiple semiconductor devices may be fabricated in an arrangement on a single semiconductor wafer and then separated into individual semiconductor devices.
Metrology processes are used at various steps during semiconductor manufacturing to monitor and control the process. Metrology processes are different than inspection processes in that, unlike inspection processes in which defects are detected on wafers, metrology processes are used to measure one or more characteristics of the wafers that cannot be determined using existing inspection tools. Metrology processes can be used to measure one or more characteristics of wafers such that the performance of a process can be determined from the one or more characteristics. For example, metrology processes can measure a dimension (e.g., line width, thickness, etc.) of features formed on the wafers during the process. In addition, if the one or more characteristics of the wafers are unacceptable (e.g., out of a predetermined range for the characteristic(s)), the measurements of the one or more characteristics of the wafers may be used to alter one or more parameters of the process such that additional wafers manufactured by the process have acceptable characteristic(s).
In semiconductor metrological tomography, a free-form scattering density map (SDM) is determined from diffracted light from a periodic planar target. For hard x-rays, this scattering density is a complex number representing a real part that is the deviation from unity of the index of refraction and an imaginary part that is the index of extinction. Upon a constant inverse scaling involving the classical electron radius multiplied by the x-ray wavelength squared divided by 2π, the real part of the SDM is equivalent to the electron density of the material. As such, the term electron density is often used as an ersatz definition for scattering density. Density determination is the result of an optimization process that matches simulated and measured diffraction patterns while regularizing the SDM. The SDM takes the form of a set scattering densities assigned to volume elements (voxels) that tile the scattering volume of the x-ray target, typically a periodic unit cell in the planar (x, y) directions and the typically non-periodic scattering region perpendicular to it (z). This scattering volume is denoted as the extended unit cell.
One of the disadvantages of techniques that attempt to infer the SDM from diffracted light intensities is that there is no absolute or relative phase information available in the measurement. As such, there is no mechanism to uniquely determine the SDM. Indeed, there are many instances of the SDM that can produce precisely the same diffracted light signal. Furthermore, the height dependency on the location of the scattering volume is weak in the hard x-ray spectra. Because of this, several ambiguities arise in the resolved SDM, including translational, space fraction, and vertical inversion ambiguities. With the translational ambiguity, the SDM may be shifted in any direction without a change in the simulated measurement, thus having no effect on the constraint. With the space fraction ambiguity, two separate geometries in simple structures can produce the same scattering profiles for all orders except for the zeroth order. With vertical inversion ambiguity, the single scattering model produces the same simulated spectra if the SDM is flipped with respect to a horizontal plane.
The previous techniques attempted to resolve the lack of phase by, in a sense, borrowing phase from the SDM initial condition and/or penalizing the difference in the optimization between the resolved SDM and the initial SDM. Inducing the phase from the initial condition, however, can skew the estimated SDM toward the initial SDM. This can produce features in the estimated SDM that would not otherwise be there or suppress geometric features which should be there.
Therefore, improvements in metrology are needed.